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# Assume the function f(x) is defined as follows: f(x) =

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Assume the function f(x) is defined as follows: f(x) = [#permalink]  22 Jul 2019, 02:51
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Assume the function f(x) is defined as follows: $$f(x) = (x – 4)^2 + \sqrt{x+3} + \frac{5}{x+2}$$. For which of the following values of x is f(x) defined?

Indicate all such values.

A. –5

B. –4

C. –3

D. –2

E. –1
[Reveal] Spoiler: OA

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Re: Assume the function f(x) is defined as follows: f(x) = [#permalink]  24 Jul 2019, 10:24
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here we need to consider two constraints.
We can't have square root of negative numbers. So, x+3 >=0 or, x>= -3
We can't have denominator 0. So x+2 not equal i.e. x not equal -2

From first constraint, we get values -3, -2, -1. But from the second constraint, we have to exclude -2. Thus, -3 and -1 are our answers.
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Re: Assume the function f(x) is defined as follows: f(x) = [#permalink]  30 May 2020, 11:56
What does it mean to be undefined?

There are a lot of situations that are undefined, but two of the most common in GRE-level math are 1) taking the square root of a negative number and 2) dividing by zero.

For each of the items being added up, you only have to look at two: sqrt(x+3) and 5/(x+2)

For the first, x has to be greater than or equal to -3 in order to not be a negative number under the square root sign. Eliminate A and B.

For the second, x cannot be equal to -2 so that you're not dividing by zero. Eliminate D.

For the values of X for answers C and E, you've got a defined equation. Those are the answers!
Re: Assume the function f(x) is defined as follows: f(x) =   [#permalink] 30 May 2020, 11:56
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